Damage-resistant glass articles and method

ABSTRACT

A strengthened glass article has opposing first and second compressively stressed surface portions bound to a tensilely stressed core portion, with the first surface portion having a higher level of compressive surface stress than the second surface portion for improved resistance to surface damage, the compressively stressed surface portions being provided by lamination, ion-exchange, thermal tempering, or combinations thereof to control the stress profiles and limit the fracture energies of the articles.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority under 35 U.S.C. §119(e)of U.S. Provisional Application Ser. No. 61/334699 filed on May 14,2010.

FIELD OF THE DISCLOSURE

The present disclosure relates to strengthened glass articles, and moreparticularly to glass articles produced by strengthening opposing glasssurfaces of the articles by unequal amounts.

TECHNICAL BACKGROUND

The strengthening of glass articles through the introduction ofcompressive stresses into the surfaces of the articles can beaccomplished by thermal tempering, ion-exchange or chemical tempering,and the lamination of glass surface layers to glass core layers. Thermaltempering involves rapidly cooling the surfaces of a hot glass articleto set the surface glass while allowing the core glass to contractthrough slower cooling. Ion-exchange strengthening or so-called chemicaltempering typically involves exchanging large mobile ions from thesurfaces of the glass with smaller ions in the interior of glass whichcan introduce compressive stresses into the glass surfaces. In laminarstrengthening, glass surface layers or skins of relatively low thermalexpansion are fused to glass core layers of relatively high thermalexpansion so that compressive stress can develop in skins as thelaminated articles are cooled following fusion.

While each of these known methods of glass strengthening has beenemployed successfully to improve the suitability of glass for a numberof existing technical applications, new applications have imposed higherdemands on the ability of glass materials to resist surface damage inuse. In some flat glass applications, for example, the damage resistanceof one of the surfaces of the glass needs to be superior to the damageresistance of the other surface, because one of the surfaces sees moreabuse in day-to-day use than the other surface. Touch screen displaysare an example of an application where increased surface damageresistance in the active or exposed surface of the displays is presentlyrequired.

In most instances the known methods of glass strengthening have beenused to induce uniform compressive stresses and uniform depths ofsurface compression on each of the two surfaces of the glass articlebeing strengthened. While resistance to surface damage can be improvedin some cases through modifications of these methods to increase thelevels of surface compression in the articles, the results are notsatisfactory for a number of applications. One disadvantage, forexample, is that increasing surface compression can correspondinglyincrease core tension. High core tensions in strengthened glass articlescan undesirably increase the fracture energy of the article in the eventof breakage.

SUMMARY

In accordance with the present disclosure, strengthening methods areemployed to provide glass articles wherein one surface, termed theprimary surface, is provided with a higher level of surface compressionand/or a higher depth of surface compression layer than the othersurface. The primary surface will serve as the surface exposed to moresevere or frequent damage in service. A particular advantage of thisso-called asymmetric strengthening is that better control over theproperties of the asymmetrically strengthened article, such as forexample the level of compression in the opposing surfaces and the levelof tensile stress in the core of the article, can be effectivelycontrolled.

In a first aspect, therefore, the present disclosure encompasses a glassarticle having opposing first and second compressively stressed surfaceportions bound to a tensilely stressed core portion, wherein the firstsurface portion has a higher level of surface compression than thesecond surface portion. Such glass articles are thus asymmetricallystrengthened, with asymmetric surface stresses and asymmetric stressprofiles across the thickness of the articles.

In some embodiments according to the present disclosure the surfacecompression in at least the first surface portion of a disclosed articleis produced by thermal tempering; in other embodiments the surfacecompression is developed through differential ion-exchange treatment ofopposing surfaces. Further embodiments include those wherein at leastthe first surface portion of the strengthened article comprises a layerof glass having a composition differing from a composition of the coreportion; such embodiments can be provided, for example, by anion-exchange treatment of at least the first surface portion or byforming that surface portion through the fusion of a layer of skin glassto the core glass of the article.

BRIEF DESCRIPTION OF THE DRAWINGS

The articles and methods disclosed herein are further described belowwith reference to the appended drawings, wherein:

FIG. 1 is a schematic orthogonal view of a flat glass plate;

FIG. 2 is an edge view of a glass plate showing a temperature profile;

FIG. 3 is a diagram presenting stress profiles for thermally temperedglasses;

FIG. 4 is a diagram plotting tempering stress versus cooling rate for aglass surface;

FIG. 5 is a diagram presenting stress profiles for ion-exchangedglasses;

FIG. 6 is a diagram plotting total stress versus surface thickness forlaminated glasses; and

FIG. 7 is a schematic elevational cross-section of a laminated glass.

DETAILED DESCRIPTION

In general, the commercial tempering of silicate glass articles of plateand tube configuration involves the symmetric cooling of the articlesfrom temperatures above the transformation range of the glass to roomtemperature. The resulting stress profiles are parabolic through thethickness of the article, with levels of surface compression being abouttwice the level of central tension. The magnitude of the central tensiondepends linearly on the cooling rate R and thermal expansivity α′ of theglass, quadratically on the thickness t of the glass, and inversely onthe thermal diffusivity k of the glass, with the depth of the resultingsurface compression layers being about 21% of the thickness t. Incertain embodiments according to the present disclosure, glass articleswith opposing compressively stressed surfaces of differing compressivestress level are provided through asymmetric thermal tempering, suchthat both major surface portions of the articles are thermally tempered,but to different degrees.

For example, the rates of cooling used to temper the opposing surfacescan be unequal, with the first surface of the article being cooled morerapidly than the second surface. The second surface may be cooled moreslowly than the first surface, or it may be otherwise treated, e.g., byion-exchange or other means, to develop a level of compressive stressthat is less than that of the first surface. Asymmetric temperingenables improved control over surface compressive stress levels anddepths of compression layer, thus enhancing resistance to surface damageand with only minimal changes in stored tensile energy, i.e. fractureenergy, and in warping tendency.

The heat transfer equations applicable to thermal tempering can beextended to asymmetric tempering both for flat plates (Cartesiancoordinates) and for cylindrical tubes (polar coordinates). Thefollowing equations apply to the case of a glass plate where bothsurfaces are thermally tempered, but where the cooling rates for the twosurfaces are unequal.

The classical differential equation for heat transfer during the coolingof a flat glass plate is given by:

$\begin{matrix}{{\frac{\partial\;}{\partial z}\left( {K\frac{\partial T}{\partial z}} \right)} = {\rho \; c_{p}\frac{\partial T}{\partial t}}} & (1)\end{matrix}$

and that for a circular glass tube by:

$\begin{matrix}{{\frac{1}{r}\frac{\partial\;}{\partial r}\left( {{Kr}\frac{\partial T}{\partial r}} \right)} = {\rho \; c_{p}\frac{\partial T}{\partial t}}} & (2)\end{matrix}$

where T denotes temperature, t the time, K the thermal conductivity, ρthe density, c_(p) the specific heat, z the thickness coordinate for theflat plate. Assuming a constant cooling rate R typical of a conventionalcommercial tempering process, the solution of eqn. (1) subject toboundary conditions T=T_(i) at t=0 is given by

T(z)=T _(i)+(R/2k)z ²  (3)

wherein k is the thermal diffusivity of the glass, defined as(K/ρc_(p)).

FIG. 1 of the drawings presents an isometric view of a flat glass platesection 10 of thickness h in the x-y-z coordinate system. Where such aplate section is cooled symmetrically on both of surfaces S1 and S2, thetemperature profile through its thickness is parabolic and the averagetemperature, obtained by integrating eqn. 3 from z =−0.5h to z=0.5h, isfound to be:

T _(av) =T _(i)+[Rh ²/24k  ](4)

The resulting tempered glass stress distribution through the thicknessof plate section 10 is symmetric, and given at any location z across theplate thickness by:

ρ(z)={Eα′/(1−ν)}[T(z)−T _(av)  ](5)

wherein α′ denotes the expansivity or coefficient of thermal expansionof the glass in the glass transformation range, E is the Young's Modulusof the glass, and ν is the Poisson's Ratio for the glass. Equation (5)satisfies force equilibrium in the z direction. The surface compressionσ_(s) and the center tension σ_(c) within the mid-plane of the glassplate (indicated by the broken line at Z=0 in FIG. 1), follow from eqn.5, namely

σ(+/−0.5h)=σ_(s) =˜{Eα′/(1−ν)}[h ² R/(12k)]  (6a)

σ(0)=σ_(c) ={Eα′/(1−ν)}[h ² R/(24k)]  (6b)

Equations (6a) and (6b) confirm that the center tension is one-half ofsurface compression for a symmetrically cooled plate. Further, settingequation (5) to zero yields the depth of compression layer δ as:

δ=0.21h  (7)

The substantial depth of compression secured through thermal temperingis achieved without excessive center tension, a particularlyadvantageous feature where both surface damage protection and a lowfracture energy are required.

In the case of asymmetric tempering, the cooling rate is different oneach of the two surfaces. For example, cooling may be at a rate of R₁ ona surface S1 of a plate 10 such as shown in FIG. 1 of the drawing, and alower rate of R₂ on surface S2 of that plate. FIG. 2 of the drawingsprovides a schematic illustration of a cross-section of a glass platesuch as a plate 10 upon which are superimposed temperature profilecurves that are representative of profiles that can be developed throughthe use of differential cooling rates. As shown in FIG. 2, plate 10 hasa thickness h as measured along the horizontal z axis extending fromorigin O, with relative glass temperatures being reported on verticalaxis T extending from the origin and lying in the mid-plane of platethickness h.

The temperature profiles across glass plate 10 that result from coolingthe two plate surfaces S1 and S2 at two different rates R₁ and R₂ areparabolic and asymmetric, consisting of two different parabolas P1 andP2. Those parabolas merge at z=z_(o), i.e., in a plane parallel with butoffset from the mid-plane of plate 10 by a distance z_(o). The highercooling rate R₁ cools a larger thickness of plate 10 (0.5h+z_(o)), whilethe lower cooling rate R₂ cools a smaller thickness of the plate(0.5h−z_(o)).

Continuity conditions require that both the temperature T and thetemperature gradient at z=z_(o) be identical, whether derived fromparabola P1 or parabola P2. Therefore,

T ₁(−z _(o))=T ₂(−z_(o))=T _(i), and

dT ₁ /dz(−z _(o))=dT ₂ /dz(−z _(o))=0

Integrating the second equation above once, we obtain:

dT ₁ /dz=(z+z _(o))R ₁ /k for parabola P1

dT ₂ /dz=(z+z _(o))R ₂ /k for parabola P2

where k is the thermal diffusivity of the glass as above described.Further integration then yields:

T ₁(z)=T _(i)+(z+z _(o))²(R ₁/2k), −z _(o) <z<0.5h  (8)

T ₂(z)=T _(i)+(z+z _(o))²(R ₂/2k), −0.5h<z<−z _(o)  (9)

with equations 8 and 9 satisfying the required continuity conditions.The average temperature of such an asymmetrically cooled plate is givenby

T _(av) =T _(i)+(R ₁/6kh)(0.5h+z _(o))³+(R ₂/6kh)(0.5h−z _(o))³  (10)

while the equations for the resulting tempering stresses σ₁ and σ₂ asfunctions of plate cross-sectional locations z over parabolic regions P1and P2 are, respectively:

σ ₁(z)={Eα′/(1−ν)}(R ₁/6kh)[{3h(z+z _(o))²−(o.5h+z _(o))³−λ(0.5h−z_(o))³)}], −z _(o) <z<0.5h  (11)

σ ₂(z)={Eα′/(1−ν)}(R ₂/6kh)[{3h(z+z _(o))²−(0.5h−z _(o))³−(0.5h+z_(o))³/λ}], −0.5h<z<−z _(o)  (12)

wherein λ=R₂/R₁, the ratio of the plate surface cooling rates.

The surface compressions and stress distributions achievable throughasymmetric tempering at a selected cooling rate ratio can be determinedby measurement or calculation for any particular glass compositionselected for fabricating a glass article in accordance with the presentdisclosure. FIG. 3 of the drawing compares the calculated stress profileof a symmetrically tempered glass plate with the calculated stressprofiles for three asymmetrically tempered plates, all four plates beingof identical 3-mm thickness and soda-lime silicate glass composition.The relevant physical properties of the glass selected for thecomparisons in FIG. 3 are reported in Table 1 below.

TABLE 1 Typical Physical Properties-Soda-Lime Silica Glass Young'sModulus E (GPa) 72 Poisson's Ratio ν 0.22 Coeff. Thermal Expansion α'(cm/cm/C.) 11 × 10⁻⁶ Thermal Diffusivity k (cm²/sec) 0.0084

The symmetrically tempered glass plate (curve 10 a in FIG. 3) has astress profile produced by cooling both surfaces of the plate at acooling rate of −90° C./sec. (i.e., R₁=R₂, or a cooling rate ratio of1.0). The three asymmetrically tempered plates are tempered at coolingrate ratios R₂/R₁ of 0.9, 0.8 and 0.7 (Curves 10 b, 10 c and 10 d,respectively). As the curves in FIG. 3 reflect, the use of cooling rateratios increasingly below 1.0 produces increasing levels of compressivestress (higher negative values of σ₁ at plate surface S1), together withincreasing depths of compression layer (peak tensile stress planesshifted toward negative values of z). As can be seen from FIG. 3, thedepth of compression layer is larger for surface S1 that experiences thehigher cooling rate, and vice-versa.

From data such as shown in FIG. 3 it can be determined that the ratio ofcooling rates R₂/R₁ used for asymmetric tempering should be about 0.7 orgreater, to avoid the possibility of developing tensile stress at themore slowly cooled plate surfaces. As is known, glass fracture caneasily be initiated from surface flaws present on glass surfaces thatare placed under tension.

Yet another consideration for the case of asymmetric tempering arisesfrom the fact that asymmetric levels of surface compression can causewarpage of flat glass plates, if the plates are thin and the edges ofthe plates are not constrained. However, the warp magnitudes aregenerally small, the warp or sagitta being readily estimated from theequation:

s=e ²/8ρ  (13)

wherein e denotes the length of the plate and ρ its radius of curvature.The radius of curvature depends on the elastic properties of the glassaccording to the equation:

ρ={Eh ³/(1−ν²)}/12M  (14)

wherein M, the bending moment responsible for warp, is given by

M={Eα′/(1−ν)}(R ₁/6k)[( 3/64)h ⁴+(¼)z _(o) h ³+(⅜)z _(o) ² h ²−(¼)z _(o)⁴−(R ₂ /R ₁){( 3/64)h ⁴−(¼)z _(o) h ³+(⅜)z _(o) ² h ²−(¼)z _(o) ⁴⁴}]  (15)

In asymmetrically tempered plates wherein the plate edges areconstrained from warping, a bending moment with sign reversed fromequation (15) is introduced at plate edges. That bending moment reducescompressive stress on one plate surface while adding a similar amount ofcompressive stress on the other surface.

The advantages of asymmetric tempering and surface compression are notlimited to glass articles of plate-like configuration, but extend toother shapes, such as cylindrical glass tubes, as well. The integrationand analysis of differential heat transfer equations by steps analogousto those for the case of asymmetric plate cooling as disclosed abovepermit calculations of the asymmetric stress profiles resulting from thecooling of the interiors and exteriors of glass tubes at differingcooling rates. Embodiments of the presently disclosed glass articlesthat comprise asymmetrically tempered tubing wherein high surfacecompression is developed in exterior tubing surface offer particularadvantages where protection from exterior tubing damage is required.

The case of glass tubing of soda-lime silica composition with innerradius a=2.5 cm and outer radius b=2.7 cm is illustrative. Starting at auniform initial glass tubing temperature of 650° C., the outer surfacesof a series of glass tubes are cooled at a cooling rate 90° C./sec(R_(o)=−90) while the inner surfaces are cooled at one of a series oflower cooling rates R_(i). Cooling rate ratios R_(i) /R_(o) in the rangeof 0.1 to 1.0 are selected for analysis.

The asymmetric stress profiles calculated from such differentialtempering treatments are reflected in FIG. 4 of the drawings. FIG. 4presents curves plotting surface stress levels for the inner surfaces(curve Si) and outer surfaces (curve So) of each of the series ofasymmetrically tempered tubes. The applicable cooling rate ratiosR_(i)/R_(o) are shown on the horizontal axis and the resulting surfacestress levels in MPa on the vertical axis, with the more negative stresslevel values representing higher surface compression in accordance withconvention.

The outer surface (So) stress levels in FIG. 4 indicate that outersurfaces of the tubes are always in compression, with rapidly increasingcompressive stress levels being achievable at lower cooling rate ratios.The inner surface (Si) stress levels, on the other hand, begin todecrease at similarly rapid rates, such that inner tubing surfaces beginto experience tension at cooling ratios below about 0.6. Thus insuringsurface compression on both tubing surfaces generally requires thatcooling rate ratios of at least 0.6 be employed.

The depths δ of the surface compression layers developed on theabove-described tubing samples can also be calculated from theproperties of the glass and the heat transfer equations. Table 2 belowsets forth inner surface (Si) and outer surface (So) compression layerdepth values δ for those members of the series of asymmetricallytempered tubes of soda-lime silica composition yielding surfacecompression layers on both inner and outer tube surfaces within thegiven range of cooling rate ratios R_(i) /R_(o).

TABLE 2 Compression Layer Depths-Tempered Glass Tubing R_(i)/R_(o) δ-So(mm) δ-Si (mm) 1.0 0.43 0.40 0.9 0.45 0.38 0.8 0.52 0.26 0.7 0.56 0.160.6 0.62 0.01

As the Table 2 data suggest, the greater compression layer depths δ onouter tubing surfaces (So), ranging from 0.43 mm to 0.63 mm, result fromthe higher surface cooling rates for those surfaces, whereas the innersurface compression layer depths δ range from 0.40 to as little as 0.01mm.

Among the further embodiments of the presently disclosed glass articlesare articles wherein the surface compression in at least one of theopposing compressively stressed surface portions surrounding thetensilely stressed core portion is produced by an ion-exchangetreatment. Ion-exchange treatments, including treatments wherein thesurface compression in both surface portions is developed through ionexchange treatments of both surface portions, but to differing degrees,enable the development of asymmetrically compressively stressed surfacelayers that can exhibit stress profiles and depths of surfacecompression quite different from those produced by asymmetric thermaltempering, and advantageous for certain applications. A naturalconsequence of such asymmetric ion-exchange strengthening is that theopposing surface portions of the article have compositions differingfrom each other as well as from the core portion of the article.

As was the case for asymmetric thermal tempering, equations enabling thecalculation of compressive stress levels and depths of surfacecompression for glass plates or sheets can be derived from thefundamental differential equation governing transport of mobile ions inglasses, conventionally given by:

$\begin{matrix}{{{\frac{\partial\;}{\partial z}\left( {D\frac{\partial C}{\partial z}} \right)} = \frac{\partial C}{\partial t}},} & (101)\end{matrix}$

wherein D is the ion diffusion coefficient for the selected glass andthe selected ion (eg., Na, K, Li, etc.), C is the concentration of theexchanged ions, z is the thickness coordinate for a flat glass plate orsheet, and t is the ion diffusion time. The boundary conditions forsolving equations (101) are:

C=C₁ at z=h/2 (top surface), and

C=C₂ at z=−h/2 (bottom surface)  (102)

with the initial condition everywhere in the plate being:

C=C_(o) at t=0  (103)

and therefore that:

C_(o)<C₁ and

C_(o)<C₂

Concentration equations for symmetric ion-exchange wherein the ionconcentrations at top and bottom surfaces are the same (C₁=C₂) have beenreported . In the symmetric case the notation C₁ can be used for bothsurface concentrations. A simple known method of obtaining a solution isto use a similarity transport. An expression for concentration in theupper half of glass plate becomes:

$\begin{matrix}{\frac{{C(z)} - C_{o}}{C_{1} - C_{o}} = {{1 - {{{erf}\left( \frac{{h/2} - z}{\sqrt{4\; {Dt}}} \right)}\mspace{14mu} {for}\mspace{14mu} {h/2}}} > z > 0}} & (104)\end{matrix}$

where erf denotes the error function. The error function is defined as:

$\begin{matrix}{{{erf}(\eta)} = {\frac{2}{\pi}{\int_{0}^{\eta}{{\exp \left( {- \xi^{2}} \right)}\ {\xi}}}}} & (105)\end{matrix}$

with erf(0)=0, and erf(1)=0.8427. Similarly, an expression forconcentration in the lower half of glass plate is given by:

$\begin{matrix}{\frac{{C(z)} - C_{o}}{C_{1} - C_{o}} = {{1 - {{{erf}\left( \frac{{h/2} + z}{\sqrt{4\; {Dt}}} \right)}\mspace{14mu} {for}\mspace{14mu} 0}} > z > {{- h}/2}}} & (106)\end{matrix}$

Since the concentration C(z) is a known function of z, the averageconcentration C_(av) can be obtained by integrating from z=h/2 to z=−h/2:

$\begin{matrix}{C_{av} = {C_{o} + {4\left( {C_{1} - C_{o}} \right)\sqrt{\frac{k}{\pi}}}}} & (107)\end{matrix}$

where k=Dt/h².

The ion-exchange stress distribution through the thickness is symmetricand given by known equation (108) at any location z across the platethickness:

$\begin{matrix}{{{\sigma (z)} = {- {\frac{EB}{1 - \upsilon}\left\lbrack {{C(z)} - C_{av}} \right\rbrack}}},} & (108)\end{matrix}$

where B denotes the lattice dilation constant and B[C(z)−C_(av)]represents the uniaxial strain induced by ion-exchange. Equation (108)satisfies force equilibrium in the z direction.

The surface compression σ_(s) and center tension o then follow fromequation (108), namely

$\begin{matrix}{{\sigma \left( {\pm \frac{h}{2}} \right)} = {\sigma_{s} = {{- \frac{EB}{1 - \upsilon}}\left( {C_{1} - C_{av}} \right)}}} & \left( {109a} \right) \\{{\sigma (0)} = {\sigma_{c} = {{- \frac{EB}{1 - \upsilon}}\left( {C_{o} - C_{av}} \right)}}} & \left( {109b} \right)\end{matrix}$

As equations (109a) and (109b) suggest, the ratio of the center tensionand surface compression is the ratio of the concentration differencebetween the plate mid-plane and plate surfaces relative to the averageconcentration for the ion-exchanged plate. Setting equation (109a) tozero yields the depth of compression layer δ, which may be obtainednumerically using the known values of C_(o) and C₁.

For the case of asymmetric ion-exchange, the exchanged ion concentrationis different at each of the two surfaces, defined as C₁ at top surfaceS1 and C₂ at bottom surface S2. The quantities C₁ and C₂ are constant.The concentration profile, which is no longer symmetric, consists of twoerror functions which merge at z=z_(o). The error function for C₁ isvalid from z=h/2 to mid-plane location z=z_(o) and that for C₂ is validfrom z=z_(o) to z=−h/2. The location z_(o) is obtained by assuming thatthe depth over which the surface concentration (C₁ or C₂) has an effectis proportional to the concentration difference:

$\begin{matrix}{\frac{_{1}\;}{_{2}\;} = {\frac{{h/2} - z_{o}}{z_{o} + {h/2}} = \frac{C_{1} - C_{o}}{C_{2} - C_{o}}}} & (112)\end{matrix}$

where d₁ and d₂ are the depths affected by C₁ and C₂, respectively.Equation (112) can be solved for z_(o):

$\begin{matrix}{z_{o} = {\frac{h}{2}\left( \frac{C_{2} - C_{1}}{C_{1} + C_{2} - {2\; C_{o}}} \right)}} & (113)\end{matrix}$

As expected, for C₁>C₂, z_(o) is negative meaning that C₁ has effect toa greater depth (more than h/2) and vice versa. In this case,expressions for concentration are given by:

$\begin{matrix}{\frac{{C(z)} - C_{o}}{C_{1} - C_{o}} = {{1 - {{{erf}\left( \frac{{h/2} - z}{\sqrt{4\; {Dt}}} \right)}\mspace{14mu} {for}\mspace{14mu} {h/2}}} > z > z_{o}}} & \left( {114\; a} \right) \\{\frac{{C(z)} - C_{o}}{C_{2} - C_{o}} = {{1 - {{{erf}\left( \frac{{h/2} + z}{\sqrt{4\; {Dt}}} \right)}\mspace{14mu} {for}\mspace{14mu} z_{o}}} > z > {{- h}/2}}} & \left( {114\; b} \right)\end{matrix}$

The average concentration for asymmetric ion-exchange is readilyobtained by integration over the glass thickness:

$\begin{matrix}{C_{av} = {C_{o} + {2\left( {C_{1} + C_{2} - {2\; C_{o}}} \right)\sqrt{\frac{k}{\pi}}}}} & (115)\end{matrix}$

Similarly, the asymmetric surface stress profiles are given by

$\begin{matrix}{{\sigma (z)} = {{{- \frac{EB}{1 - \upsilon}}\left( {C_{1} + {\left( {C_{o} - C_{1}} \right)\left( {{erf}\left( \frac{{h/2} - z}{\sqrt{4\; {Dt}}} \right)} \right)} - C_{av}} \right)\mspace{14mu} {for}\mspace{14mu} {h/2}} > z > z_{o}}} & \left( {116\; a} \right) \\{{\sigma (z)} = {{{- \frac{EB}{1 - \upsilon}}\left( {C_{2} + {\left( {C_{o} - C_{2}} \right)\left( {{erf}\left( \frac{{h/2} + z}{\sqrt{4\; {Dt}}} \right)} \right)} - C_{av}} \right)\mspace{14mu} {for}\mspace{14mu} z_{o}} > z > {{- h}/2}}} & \left( {116\; b} \right)\end{matrix}$

where the expressions for C(z) are substituted from equations (114a) and(114b) into equation (108).

FIG. 5 of the drawings compares stress profiles for a symmetricallyion-exchanged 1-mm thick glass plate with C₁=C₂=13.23 mol % (curve 100a) against three asymmetrically ion-exchanged glass plates. Stresslevels (σ) are reported in MPa on the vertical graph axis and platecross-sectional location z on the horizontal axis. The asymmetricallyion exchanged plates are of the same geometry and base glass compositionand have the same first surface (S1) exchanged ion concentration as thesymmetrically ion-exchanged plate, but with varying lower exchanged-ionconcentrations on the second plate surface (S2), i.e., with C₁=13.23 mol% and C₂=10.23, 5.23, or 2.7 mol % (curves 100 b, 100 c and 100 d,respectively). The exchanged-ion concentration in the base glasscomposition (C₀) is 2.55 mol %. The physical properties of the baseglass and the diffusion time (t) employed to reach the C₁ exchanged-ionconcentration are reported in Table 3 below.

TABLE 3 Physical properties and ion-exchange parameters Young's ModulusE (MPa) 72900 Poisson's Ratio ν 0.211 B (m/m/mol %)  11 × 10⁻⁶Diffusivity D (m²/sec)  1.1 × 10⁻¹⁴ t, sec 28800 Thickness, mm 1

As the stress profile curves in FIG. 5 reflect, decreasing exchanged-ionconcentrations at S2 result in decreasing S2 compressive stress levels σand decreasing depths δ of compression layer at that surface, althoughthe difference in compression layer depths δ_(t) and δ_(b) as betweenthe top and bottom surfaces is not large. For example, where the ratioof exchanged-ion concentration (C₁) at top surface S1 to theexchanged-ion concentration (C₂) at bottom surface S2 is about 0.6, thetop surface compression level is approximately 800 MPa and the bottomsurface compression level is approximately 400 MPa. At those compressionlevels the depths of the compression layers are approximately 0.054 mmand 0.047 mm, respectively. Thus both surfaces incorporate relativelydeep compression layers, a characteristic that is particularlyadvantageous when protection against bottom surface as well as topsurface damage is required.

The analyses of asymmetric ion-exchange strengthening set forth above donot account for plate bending contributions since the plates beingcharacterized are not edge-constrained. As was the case for asymmetricthermal tempering, edge constraints will modify the stress distributionprofile of a glass plate comprising ion-exchanged surface compressionlayers, generally by increasing surface compression on the plate surfacehaving the highest unconstrained compressive stress level and decreasingsurface compression on the opposite plate surface. However, for the caseof asymmetric ion-exchange strengthening, analyses based on the elasticproperties of glass indicate that, even for modest plate thicknesses,warp is sufficiently small that it is not problematic for mostapplications.

Still further embodiments of the presently disclosed glass articles arearticles provided by laminating the surface portions to a glass corediffering in composition and physical properties from the surfaceportions, but wherein the laminated surface portions exhibit differinglevels of compressive stress. For example, asymmetric laminationembodiments can provide glass articles wherein the opposingcompressively stressed surface portions joined to the tensilely stressedcore are of differing thicknesses, or differing compositions and thermalexpansivities, thus providing compressive stress in a first surfaceportion that differs from the compressive stress in a second surfaceportion. The characteristics of such articles compare favorably withthose of articles comprising asymmetric cross-sectional stress profilesprovided by thermal or chemical ion-exchange tempering or strengthening,and offer further advantages for certain applications.

For purposes of the following analysis reference is made to FIG. 7 ofthe drawings schematically showing an elevational diagram of a laminatedarticle, not in true proportion or to scale. The article comprises afirst surface layer or skin L1, a core layer L2, and a second surfacelayer or skin L3, those components being of thicknesses h₁, h₂ and h₃respectively.

Embodiments of laminated glass articles in accordance with the presentdescription include those wherein both of the surface or skin portionsor layers of the laminate are composed of the same glass, but whereinthe thickness of one skin layer differs from that of the other skinlayer. In those embodiments each of the three glass layers (firstsurface layer L1, core layer L2 and second surface layer L3) willexperience bending moments M₁, M₂, and M₃ respectively, due to thediffering direct compressive forces N₁ and N₃ and tensile force N₂ thatdevelop in the skins and core, respectively, during the cooling andcontraction of the layers of the article following high-temperaturelamination. Again the unconstrained laminates will exhibit somecylindrical warping due to their asymmetric stress profiles, but theamounts of warp are generally small.

As the following analysis will show, the expressions for forces N₁, N₂,and N₃, and bending moments M₁, M₂ and M₃ developed below satisfy theapplicable force equilibrium and Moment/warp relationships, namely

N ₁ +N ₂ +N ₃=0   (201)

M ₁ +M ₂ +M ₃ =M=(1+ρ)(D ₁ +D ₂ +D ₃) /ρ  (202)

where the D values denote the bending rigidities of the layers and ρrepresents the common radius of curvature of the structure where warpingdue to asymmetric surface compression levels occurs.

The pertinent equations for direct stress (σ_(d)) and bending stress(σ_(b)) are summarized as follows:

σ_(d1) =N ₁/h₁  (203)

σ_(d2) =N ₂/h₂  (204)

σ_(d3) =N ₃/h₃  (205)

σ_(b1)=6M ₁/h₁ ²  (206)

σ_(b2)=6M ₂/h₂ ²  (207)

σ_(b3)=6M ₃/h₃ ²  (208)

wherein h₁, h₂ and h₃ are the thicknesses of the first surface layer L1,core layer L2, and second surface layer L3, respectively, and wherein

N ₁=[{(a ₃ +b ₂ +b ₃)}(α_(c)−α_(s))(T _(set)−25)]/Δ  (209)

N ₃=[{(a ₁ +b ₁ +b ₂)}(α_(c)−α_(s))(T _(set)−25)]/Δ  (210)

N ₂=−(N ₁ +N ₃)

Δ=(a₂ −b ₂)²−(a ₁ +a ₂ +b ₁(a ₂ +a ₃ b ₃)  (211)

M ₁ ={D ₁/(D ₁ +D ₂ +D ₃)}M  (212)

M ₂ ={D ₂/(D ₁ +D ₂ +D ₃)}M  (213)

M ₃ ={D ₃/(D ₁ +D ₂ +D ₃)}M  (214)

M=0.5[N ₁(h ₁ +h ₂)−N ₃(h ₂ +h ₃)]  (215)

with:

-   -   α_(c) and α_(s) being the thermal expansion coefficients of the        core and skin layers at the thermal set points of the glasses        making up those layers, and with    -   a₁, a₂, a₃, b₁, b₂ and b₃ being constants related to the skin        and core layer thicknesses h₁, h₂ and h₃, Young's Modulus E, and        Poisson's Ratios u of the core and skin glasses as:

a ₁=(1−υ)/(E ₁ h ₁)  (216)

a ₂=(1−υ)/(E ₂ h ₂)  (217)

a ₃=(1−υ)/(E ₃ h ₃)  (218)

b ₁=(h ₁ +h ₂)²/[4(1+υ)(D ₁ +D ₂ +D ₃]  (219)

b ₂=(h ₁ +h ₂)(h ₂ +h ₃)/[4(1+υ)(D ₁ +D ₂ +D ₃)]  (220)

b3=(h2+h3)2/[4(1+υ)(D1+D2+D3)]  (221)

For any particular laminated glass article of the kind herein described,the total stress in each of the three layers is simply the sum of thedirect and bending stresses in that layer. The total stresses for layersL1, L2 and L3 are given respectively by:

σ₁=(N ₁ /h ₁)+(6M ₁ /h ₁ ²)  (222)

σ₂=(N ₂ /h ₂)+(6M ₂ /h ₂ ²)  (223)

σ₃=(N ₃ /h ₃)+(6M ₃ /h ₃ ²)  (224)

For the asymmetrically stressed surface layers of the strengthenedarticles of the present disclosure, the direct stresses (N₁/h₁) and(N₃/h₃) are compressive or negative skin stresses and the direct stress(N₂/h₂) is a tensile or positive core stress. Similarly, where the firstsurface layer has a thickness h₁ that is greater than h₃, bendingmoments M₁ and M₃ have a sign such that (6M_(i)/h₁)² and (6M₃/h₃)² arecompressive or negative stresses on one of the surfaces of first andthird layers. The tensile component (6M₂/h₂)² will occur either at topof core layer L2 or the bottom of that core layer depending on whetherlayer L3 is thicker than layer L1 or vice-versa. In short, the tensilestress in the core layer is the sum of direct and bending stresses inthat layer. Advantageously, either layer L1 or layer L3 will experiencemaximum compressive stress on their exposed outer surfaces where maximumdamage resistance is desired. As noted above, the depths of surfacecompression are simply the respective thicknesses h₁ and h₃ of thecompressively stressed surface layers.

As in other asymmetrically stressed glass articles provided inaccordance with the present disclosure, unequal skin thicknesses h₁ andh₃ produce an asymmetric stress distribution that tends to warp thearticle into a cylindrical shape of radius ρ. That radius is given by

ρ=D ₁(1+υ)/M ₁ =D ₂(1+υ)/M ₂ =D ₃(1+υ)/M ₃  (225)

with the sagitta or maximum warp being given by

δ=L ²/(8ρ)  (226)

wherein L denotes the longer dimension of 3-layer laminate.

The use of the foregoing analyses to calculate the asymmetric stressdistributions that can be generated in laminated glass articles isillustrated below for the case of a three-layer article wherein thecompressively stressed surface layers are of the same composition butdifferent thicknesses. For the purpose of analysis the total thicknessof the laminated article and the thickness h₂ of the glass core are keptconstant while the skin thicknesses h₁ and h₃ are varied to determinethe effects of the asymmetric geometries on surface compression levelsand the levels of tensile stress in the core portion. As a specificexample, a laminate of 2.677 mm total thickness (h1+h2+h3) and 2.54 mmcore thickness is analyzed.

The physical properties of skin and core glasses for the laminatedarticle are set forth in Table 4 below. Included in Table 4 for each ofthe core and skin glasses are the elastic or Young's Modulus, in GPa,the Poisson's Ratio, the Glass Set Point or temperature at which theglass solidifies on cooling, in ° C., and the thermal expansion of eachglass at the Set Point.

TABLE 4 Properties of Core and Skin Glasses Young's Poisson's Glass SetThermal Expanion Glass Modulus E Ratio Point α at Set point Component(GPa) ν (° C.) (10⁻⁷/C.) Core 75.0 0.22 562 74.5 Skin 85.5 0.22 675 52.0

The glass articles evaluated included glass laminates wherein the ratioof L1 surface layer thickness to L3 surface layer thickness ranged from1 to 2. Results of these evaluations for a number of laminated glassarticles incorporating asymmetric surface layers are set forth in FIG. 6of the drawings. FIG. 6 plots the total stresses calculated on outersurfaces of layers L₁ and L₃ as well as in layer 2 for each of the threelayers for each of ten laminated articles having surface layer thicknessratios h₃/h₁ in the above range.

The total stress values plotted in FIG. 6 are combinations of the directstresses and bending stresses in each layer in accordance with the aboveanalyses. The observed trends in L1 and L3 total stress levels are duemainly to the same trends in the direct stress levels calculated forthose layers. The bending stresses in the surface layers are calculatedto be small due to the low bending rigidities (D₁ and D₃) of the surfacelayers.

Particularly advantageous features of the asymmetrically stressedlaminates of these embodiments of the present disclosure are therelatively modest center tensions maintained in the coresnotwithstanding the relatively high compressive stresses developed inthe surface layers. This combination of features provides excellentsurface damage resistance without undesirable increases in tensilelystressed fracture energy of layer L₂. It would permit the strengthenedglass articles to be scored and separated safely with little risk oflong-term fatigue of exposed edges of the separated sections. Inaddition, the maximum warp values calculated for the most highlystressed laminates, i.e., less than 0.1 mm over a 10-cm laminate span,would not be of concern for most applications.

As the foregoing analyses suggest, asymmetrically strengthened glasssheet products, including for example glass display panels or displaycover sheets, or even glass panes employed as glazing elements in otherdevices or structures, are of particular interest where the intendedapplication involves exposure to repeated physical contact or a highrisk of impact damage. For these and other applications, however, it isgenerally important that the sheet surface exhibiting the lower level ofcompressive surface stress not be subjected to tensional stress,physical tension, and that the level of tension in the core of the sheetnot be so great as to develop unacceptably high fracture energy in thestrengthened glass product.

In light of these considerations specific embodiments of the presentlydisclosed articles particularly include glass sheets having opposedcompressively stressed first and second surfaces joined to a tensileystressed interior core, wherein the first surface has a higher level ofsurface compression than the second surface, and wherein the core has atensile stress level not exceeding about 20 MPa. Embodiments of suchsheets wherein the level of compressive stress in the compressivelystressed second surface is at least 300 MPa, both for the unconstrainedsheet and for the sheet when edge-constrained to remove sheet warpingdue to asymmetric surface stresses.

Methods for making glass articles such as strengthened glass sheets orvessels in accordance with the foregoing disclosure are carried oututilizing apparatus and materials employed in the prior art fortempering, ion-exchanging and/or laminating heated or softened glasses.For the manufacture of a strengthened glass sheet having opposing firstand second compressively stressed surfaces bound to a tensilely stressedcore with the first surface having a higher level of surface compressionthan the second surface, the glass sheet is cooled from a temperatureabove the glass set point in a manner such that the first and secondsurfaces are cooled at different cooling rates. In particularembodiments, for example, the first surface of the sheet is cooled at acooling rate R₁ and the second surface is cooled at a lower cooling rateR₂, and the ratio R₂/R₁ is selected to be at least at least 0.7.

For the manufacture of strengthened glass sheet having an asymmetricstress profile via ion-exchange, a step of subjecting the first andsecond surfaces of the sheet to different ion-exchange strengtheningtreatments is used. Thus the first surface is subjected to a firstion-exchange treatment and the second surface is sequentially orconcurrently subjected to a second ion-exchange treatment differing fromthe first treatment. In particular embodiments, the first ion-exchangetreatment develops a concentration C₁ of exchanged ions in the firstsurface of the sheet and the second ion-exchange treatment develops aconcentration C₂ of exchanged ions in the second surface of the sheet,with C₁ differing from C₂ to a degree effective to develop a selectedasymmetric stress profile characterized by differing levels of surfacestress in the glass.

The manufacture of strengthened glass sheets or other articles havingasymmetric surface compression in opposing surfaces does not require theuse of only one strengthening strategy to achieve the desired stressprofiles. Rather, these strengthening methods can be advantageouslycombined to develop asymmetric profiles not achievable using any onestrategy alone.

As one example, a strengthened glass sheet having opposing first andsecond compressively stressed surfaces of differing stress level can bemade by the steps of first cooling the surfaces from a temperature abovethe glass set point to develop first and second levels of compressivestress in those surfaces, and then subjecting the first and secondsurfaces to ion-exchange strengthening to modify at least one of thefirst and second compressive stresses. At least one of these steps willbe carried out in a manner that develops a higher level of compressivestress in the first surface than in the second surface.

A further example of a combination method for making a strengthenedsheet or other article comprises a first step of laminating first andsecond glass skin layers to a glass core layer to form a laminated glasssheet having first and second levels of compressive stress in opposingfirst and second surfaces of the sheet; and a second step of subjectingthe first and second surfaces to ion-exchange strengthening to modify atleast one of the first and second compressive stresses. Again, at leastone of the two steps is conducted to develop a higher level ofcompressive stress in the first surface than in the second surface.

Yet another embodiment of a combination method for manufacturing astrengthened glass sheet having a first surface having a higher level ofsurface compression than a second surface comprises the steps oflaminating first and second glass skin layers to a glass core layer toform a laminated glass sheet having first and second levels ofcompressive stress in opposing first and second surfaces of the sheet,and then cooling the first and second surfaces from a temperature abovethe set points of the surfaces to modify at least one of the first andsecond compressive stresses. Either the lamination step, or the coolingstep, or both, will be carried out in a way that develops a higher levelof compressive stress in the first surface than in the second surface.

Further embodiments of the disclosed asymmetrically stressed glassarticles include articles essentially free of stress-induced warpingthat still retain an asymmetric stress profile. As above equation (226)suggests, sagitta or maximum warp δ vanishes when the radius ofcurvature ρ of a surface-stressed article approaches infinity, i.e.,when bending moment M from equation (202) above approaches zero. Ofcourse a trivial solution meeting those conditions is that of asymmetrical laminate with opposing surface portions (e.g., skin glasslayers) of identical thickness and composition. In that case the thermalexpansions and elastic moduli of the layers are necessarily the same,such that no asymmetric stress profile is present.

In accordance with the present disclosure, however, articlessubstantially free of stress-induced warping, but still offeringasymmetric stress profiles, are provided through the use of opposingfirst and second compressively stressed surface portions that differ inboth composition and thickness. The compositions and thicknessesselected are those effective to generate differing surface compressionlevels, but that do not introduce changes in curvature or flatness inthe stressed articles. Examples include surface-stressed articles suchas laminated articles that have a bending moment M as defined by theexpression M=(1+ρ)(D₁+D₂+D₃)/ρ of substantially zero, wherein D₁, D₂ andD₃ correspond, respectively, to the bending rigidities of the firstsurface portion, a glass core, and a second surface portion, and whereinp represents the common radius of curvature of the stressed articlearising from warping due to asymmetric surface compression levels.

To arrive at a numerical expression defining the thicknesses, thermalexpansions, and elastic moduli suitable for providing such articles, theexpressions for N₁ and N₃ from equations (209) and (210) above aresubstituted into equation (215) above to yield:

(h ₁ +h2)(a3+b ₂ +b ₃)(α_(c)−α_(s1))=(h ₂ +h ₃)(a ₁ +b ₁ +b₂)(α_(c)−α_(s2))  (227)

Then, setting υ₁=υ₂=υ₃=υ, which is valid for most silicate glasses, itcan be shown from equations (216) to (221) that:

a ₃ +b ₂ +b ₃ =(1−υ)[E ₁ h ₁ ³ +E ₂ h ₂ ³ +E ₃ h ₃ ³+3E ₃ h ₃(h ₁ h ₂+2h₂ ²+3h ₂ h ₃ +h ₁ h ₃ +h ₃ ²)]/Δ₁  (228)

and

a ₁ +b ₁ +b ₂ =(1−υ)[E ₁ h ₁ ³ +E ₂ h ₂ ³ +E ₃ h ₃ ³+3E ₃ h ₃(h ₁ h ₂+2h₂ ²+3h ₂ h ₃ +h ₁ h ₃ +h ₃ ²)]/Δ₂  (229)

wherein

Δ₁ =E ₃ h ₃(E ₁h₁ ³ +E ₂ h ₂ ³ +E ₃ h ₃ ³)

and

Δ₂ =E ₁ h ₁(E ₁h₁ ³ +E ₂ h ₂ ³ +E ₃ h ₃ ³)

Substituting the above expressions in equation (227) above, andsimplifying, yields the following relationship between the expansionmismatches, elastic moduli, and stressed surface portion (e.g., skinglass) thicknesses for a family of asymmetrically stressed glassarticles substantially free of surface warping:

(α_(c)−α_(s1))/(α_(c)−α_(s2))={(h ₂ +h ₃)/(h ₂ +h ₁)}[h ₁ ²+(E ₂ /E ₁)(h₂ ³ /h ₁)+(E ₃ /E ₁)(h ₃ ³ /h ₁)+3(h ₁ ²+3h ₁ h ₂ +h ₁ h ₃+2h ₂ ² +h ₂ h₃)]/[h ₃ ²+(E ₂ /E ₃)(h ₂ ³/h₃)+(E ₁ /E ₃)(h ₁ ³ /h ₃)+3(h ₃ ²+3h ₃ h ₂+h ₁h₃+2h ₂ ² +h ₂ h ₁)]  (230)

While the above equation clearly encompasses the case where h₁=h₃ andE₁=E₃, (i.e., the case of identical skin properties and skinthicknesses), a large group of asymmetrically stressed laminates orother articles wherein the thicknesses and elastic modulii of theopposing skin layers or surface portions are dissimilar is also defined.The latter group can be generally characterized as articles that includethree different glass compositions, selected to provide a highcompression first surface portion or skin, a core, and a lowercompression second surface portion or skin, such that warping of thearticle is mitigated even though at least one highly stressed, damageresistant surface layer is provided.

Of course, the foregoing descriptions and specific embodiments of thedisclosed articles and methods are presented for purposes ofillustration only, it being apparent from those descriptions that a widevariety of adaptations and modifications of those particularly disclosedembodiments may be adopted to meet the requirements of a variety ofapplications within the scope of the appended claims.

1. A glass article having opposing first and second compressivelystressed surface portions bound to a tensilely stressed core portion,wherein the first surface portion has a higher level of surfacecompression than the second surface portion.
 2. A glass articleaccording to claim 1 wherein the surface compression in at least thefirst surface portion is produced by thermal tempering
 3. A glassarticle according to claim 1 wherein the surface compression in at leastthe first surface portion is developed through an ion-exchange treatmentof the first surface portion.
 4. A glass article according to claim 3wherein the first surface portion comprises a layer of glass having acomposition differing from the composition of the second surfaceportion.
 5. A glass article according to claim 1 wherein the opposingfirst and second compressively stressed surface portions comprise firstand second glass skin layers laminated to the tensilely stressed coreportion.
 6. A glass article according to claim 5 wherein the opposingfirst and second glass skin layers are of different thickness.
 7. Aglass article according to claim 5 wherein the opposing first and secondglass skin layers are of different expansivity α′.
 8. A glass articleaccording to claim 1 wherein the opposing first and second compressivelystressed surface portions are of differing composition and thickness,and wherein the article has a bending moment M as defined by theexpression M=(1+ρ)(D₁+D₂+D₃)/ρ of substantially zero.
 9. A glass articleaccording to claim 1 having the form of a glass sheet, and wherein thetensilely stressed core portion has a tensile stress level not exceeding20 MPa.
 10. A glass article according to claim 9 wherein the level ofsurface compression in the second compressively stressed surface portionis at least 300 MPa.
 11. A method of manufacturing a strengthened glasssheet having opposing first and second compressively stressed surfacesbound to a tensilely stressed core, the first surface having a higherlevel of surface compression than the second surface, comprising atleast one of the following steps: (a) cooling the first and secondsurfaces at different cooling rates from a temperature above the setpoint of the surfaces; (b) subjecting the first and second surfaces toion-exchange strengthening treatments, with the first surface beingsubjected to a first ion-exchange treatment and the second surface beingsubjected to a second ion-exchange treatment that differs from the firstion-exchange treatment; and (c) laminating first and second glass skinlayers to a glass core layer to form a laminated glass sheet havingopposing first and second surfaces having, respectively, first andsecond levels of compressive stress in the opposing surfaces.
 12. Amethod according to claim 11 comprising the step of cooling the firstand second surfaces at different cooling rates, wherein the step ofcooling comprises cooling the first surface at a cooling rate R₁ andcooling the second surface at a lower cooling rate R₂, and wherein theratio R₂/R₁ is at least 0.7.
 13. A method according to claim 11comprising the step of subjecting the first and second surfaces toion-exchange strengthening treatments, wherein the first ion-exchangetreatment develops a concentration C₁ of exchanged ions in the firstsurface of the sheet, wherein the second ion-exchange treatment developsa concentration C₂ of exchanged ions in the second surface of the sheet,and wherein C₁ differs from C₂.
 14. A method according to claim 11comprising the steps of: (i) cooling the first and second surfaces froma temperature above the set points of the surfaces to develop first andsecond levels of compressive stress in the surfaces, and (ii) subjectingthe first and second surfaces to ion-exchange strengthening to modify atleast one of the first and second compressive stresses, wherein at leastone of steps (i) and (ii) develops a higher level of compressive stressin the first surface than in the second surface.
 15. A method accordingto claim 11 comprising the steps of: (i) laminating first and secondglass skin layers to a glass core layer to form a laminated glass sheethaving first and second levels of compressive stress in opposing firstand second surfaces of the sheet; and (ii) subjecting the first andsecond surfaces to ion-exchange strengthening to modify at least one ofthe first and second compressive stresses, wherein at least one of steps(i) and (ii) develops a higher level of compressive stress in the firstsurface than in the second surface.
 16. A method according to claim 11comprising the steps of: (i) laminating first and second glass skinlayers to a glass core layer to form a laminated glass sheet havingfirst and second levels of compressive stress in opposing first andsecond surfaces of the sheet; and (ii) cooling the first and secondsurfaces from a temperature above the set points of the surfaces tomodify at least one of the first and second compressive stresses,wherein at least one of steps (i) and (ii) develops a higher level ofcompressive stress in the first surface than in the second surface. 17.A method of manufacturing a strengthened glass sheet having opposingfirst and second compressively stressed skin layers bound to a tensilelystressed core, the first skin layer having a higher level of surfacecompression than the second skin layer, comprising the step oflaminating first and second glass skin layers of differing compositionand thickness to a glass core layer to form a laminated glass sheethaving first and second levels of compressive stress in opposing firstand second skin layers of the sheet, wherein the glass sheet has asubstantially zero bending moment M as defined by the expressionM=(1+ρ)(D₁+D₂+D₃)/ρ, wherein D₁, D₂ and D₃ correspond, respectively, tothe bending rigidities of the first skin layer, the core, and the secondskin layer, and wherein ρ represents the common radius of curvature ofthe strengthened glass sheet.